Classical approaches for implementation of FL in a wireless network suggest a separate decoding and aggregation at the PS[1]}, [2]}. This means that the PS decodes first the received local models and then combines the decoded models into a global model via a predefined aggregation policy. An alternative approach is proposed in [3]} which invokes the idea of analog function computation [4]} to perform model aggregation directly over the air. We refer to this latter approach as over-the-air FL (OTA-FL) in this paper. OTA-FL invokes the signal combination in the multiple access channel to realize the predefined aggregation policy directly over-the-air. In other words, the edge devices in OTA-FL transmit their local models with proper scaling, such the desired model aggregation is calculated from the a linearly-transformed version of the received signal at the PS. In various use-cases, OTA-FL is more efficient than separate decoding and aggregation [5]}. In fact, OTA-FL does not need to orthogonalize communication resources, i.e., allocate individual bandwidth and time slot to every device, and hence it enjoys both advantages of lower computation and resource efficiency [6]}, [7]}, [8]}.
